A discrete interaction model/quantum mechanical method for simulating nonlinear optical properties of molecules near metal surfaces

In this work, we extend the discrete interaction model/quantum mechanics (DIM/QM) method to calculate the frequency-dependent hyperpolarisabilities of molecules near metal surfaces. The DIM/QM method is a polarisable quantum mechanics/molecular mechanics method, which represents the metal surface atomistically and thus allows for explicitly modelling the influence of the local environment on the optical properties of a molecule. The interactions between the metal surface and the molecules include both the image field and local field effects. The image field effects arise from the response induced in the metal surface due to the molecules electronic charge distributions whereas the local field effects arise from interactions between the metal surface and the external light. The frequency-dependent first-hyperpolarisability is obtained in an efficient way based on time-dependent density functional theory and the (2n+1) rule. The method was tested for calculating the first-hyperpolarisability responsible for the second-harmonic generation of a fumaramide[2]rotaxane interacting with a sliver surface. The first-hyperpolarisability of the fumaramide[2]rotaxane is very small in the gas phase due to near inversion symmetry. We find that the breaking of the symmetry due to interactions with the metal surface leads to a significant induced first-hyperpolarisability. The image field effects are found to be modest and short-range. In contrast, we find that the local field effects are large and rather long-range, illustrating the importance of including these effects directly in the simulations. Comparison with experimental results shows good qualitative agreement.